Egyptian of that early day had attained a knowledge of practical mechanics which； even from the twentieth…century point of view； is not to be spoken of lightly。 It has sometimes been suggested that these mighty pyramids； built as they are of great blocks of stone； speak for an almost miraculous knowledge on the part of their builders； but a saner view of the conditions gives no warrant for this thought。 Diodoras； the Sicilian； in his famous World's History； written about the beginning of our era； explains the building of the pyramids by suggesting that great quantities of earth were piled against the side of the rising structure to form an inclined plane up which the blocks of stone were dragged。 He gives us certain figures； based； doubtless； on reports made to him by Egyptian priests； who in turn drew upon the traditions of their country； perhaps even upon written records no longer preserved。 He says that one hundred and twenty thousand men were employed in the construction of the largest pyramid； and that； notwithstanding the size of this host of workers； the task occupied twenty years。 We must not place too much dependence upon such figures as these； for the ancient historians are notoriously given to exaggeration in recording numbers； yet we need not doubt that the report given by Diodorus is substantially accurate in its main outlines as to the method through which the pyramids were constructed。 A host of men putting their added weight and strength to the task； with the aid of ropes； pulleys； rollers； and levers； and utilizing the principle of the inclined plane； could undoubtedly move and elevate and place in position the largest blocks that enter into the pyramids orwhat seems even more wonderfulthe most gigantic obelisks； without the aid of any other kind of mechanism or of any more occult power。 The same hands could； as Diodorus suggests； remove all trace of the debris of construction and leave the pyramids and obelisks standing in weird isolation； as if sprung into being through a miracle。
ASTRONOMICAL SCIENCE It has been necessary to bear in mind these phases of practical civilization because much that we know of the purely scientific attainments of the Egyptians is based upon modern observation of their pyramids and temples。 It was early observed； for example； that the pyramids are obviously oriented as regards the direction in which they face； in strict accordance with some astronomical principle。 Early in the nineteenth century the Frenchman Biot made interesting studies in regard to this subject； and a hundred years later； in our own time； Sir Joseph Norman Lockyer； following up the work of various intermediary observers； has given the subject much attention； making it the central theme of his work on The Dawn of Astronomy。＇1＇ Lockyer's researches make it clear that in the main the temples of Egypt were oriented with reference to the point at which the sun rises on the day of the summer solstice。 The time of the solstice had peculiar interest for the Egyptians； because it corresponded rather closely with the time of the rising of the Nile。 The floods of that river appear with very great regularity； the on…rushing tide reaches the region of Heliopolis and Memphis almost precisely on the day of the summer solstice。 The time varies at different stages of the river's course； but as the civilization of the early dynasties centred at Memphis； observations made at this place had widest vogue。 Considering the all…essential character of the Nile floods…without which civilization would be impossible in Egyptit is not strange that the time of their appearance should be taken as marking the beginning of a new year。 The fact that their coming coincides with the solstice makes such a division of the calendar perfectly natural。 In point of fact； from the earliest periods of which records have come down to us； the new year of the Egyptians dates from the summer solstice。 It is certain that from the earliest historical periods the Egyptians were aware of the approximate length of the year。 It would be strange were it otherwise； considering the ease with which a record of days could be kept from Nile flood to Nile flood； or from solstice to solstice。 But this； of course； applies only to an approximate count。 There is some reason to believe that in the earliest period the Egyptians made this count only 360 days。 The fact that their year was divided into twelve months of thirty days each lends color to this belief； but； in any event； the mistake was discovered in due time and a partial remedy was applied through the interpolation of a 〃little month〃 of five days between the end of the twelfth month and the new year。 This nearly but not quite remedied the matter。 What it obviously failed to do was to take account of that additional quarter of a day which really rounds out the actual year。 It would have been a vastly convenient thing for humanity had it chanced that the earth had so accommodated its rotary motion with its speed of transit about the sun as to make its annual flight in precisely 360 days。 Twelve lunar months of thirty days each would then have coincided exactly with the solar year； and most of the complexities of the calendar； which have so puzzled historical students； would have been avoided； but； on the other hand； perhaps this very simplicity would have proved detrimental to astronomical science by preventing men from searching the heavens as carefully as they have done。 Be that as it may； the complexity exists。 The actual year of three hundred and sixty…five and （about） one…quarter days cannot be divided evenly into months； and some such expedient as the intercalation of days here and there is essential； else the calendar will become absolutely out of harmony with the seasons。 In the case of the Egyptians； the attempt at adjustment was made； as just noted； by the introduction of the five days； constituting what the Egyptians themselves termed 〃the five days over and above the year。〃 These so…called epagomenal days were undoubtedly introduced at a very early period。 Maspero holds that they were in use before the first Thinite dynasty； citing in evidence the fact that the legend of Osiris explains these days as having been created by the god Thot in order to permit Nuit to give birth to all her children； this expedient being necessary to overcome a ban which had been pronounced against Nuit； according to which she could not give birth to children on any day of the year。 But； of course； the five additional days do not suffice fully to rectify the calendar。 There remains the additional quarter of a day to be accounted for。 This； of course； amounts to a full day every fourth year。 We shall see that later Alexandrian science hit upon the expedient of adding a day to every fourth year； an expedient which the Julian calendar adopted and which still gives us our familiar leap…year。 But； unfortunately； the ancient Egyptian failed to recognize the need of this additional day； or if he did recognize it he failed to act on his knowledge； and so it happened that； starting somewhere back in the remote past with a new year's day that coincided with the inundation of the Nile； there was a constantly shifting maladjustment of calendar and seasons as time went on。 The Egyptian seasons； it should be explained； were three in number： the season of the inundation； the season of the seed…time； and the season of the harvest； each season being； of course； four months in extent。 Originally； as just mentioned； the season of the inundations began and coincided with the actual time of inundation。 The more precise fixing of new year's day was accomplished through observation of the time of the so…called heliacal rising of the dog…star； Sirius； which bore the Egyptian name Sothis。 It chances that； as viewed from about the region of Heliopolis； the sun at the time of the summer solstice occupies an apparent position in the heavens close to the dog…star。 Now； as is well known； the Egyptians； seeing divinity back of almost every phenomenon of nature； very naturally paid particular reverence to so obviously influential a personage as the sun…god。 In particular they thought it fitting to do homage to him just as he was starting out on his tour of Egypt in the morning； and that they might know the precise moment of his coming； the Egyptian astronomer priests； perched on the hill…tops near their temples； were wont to scan the eastern horizon with reference to some star which had been observed to precede the solar luminary。 Of course the precession of the equinoxes； due to that axial wobble in which our clumsy earth indulges； would change the apparent position of the fixed stars in reference to the sun； so that the same star could not do service as heliacal messenger indefinitely； but； on the other hand； these changes are so slow that observations by many generations of astronomers would be required to detect the shifting。 It is believed by Lockyer； though the evidence is not quite demonstrative； that the astronomical observations of the Egyptians date back to a period when Sothis； the dog…star； was not in close association with the sun on the morning of the summer solstice。 Yet； according to the calculations of Biot； the heliacal rising of Sothis at the solstice was noted as early as the year 3285 B。C。； and it is certain that this star continued throughout subsequent centuries to keep this position of peculiar prestige。 Hence it was that Sothis came to be associated with Isis； one of the most important divinities of Egypt； and that the day in which Sothis was first visible in the morning sky marked the beginning of the new year； that day coinciding； as already noted； with the summer solstice and with the beginning of the Nile flow。 But now for the difficulties introduced by that unreckoned quarter of a day。 Obviously with a calendar of 365 days only； at the end of four years； the calendar year； or vague year； as the Egyptians came to call it； had gained by one full day upon the actual solar year that is to say； the heliacal rising of Sothis； the dog… star； would not occur on new year's day of the faulty calendar； but a day later。 And with each succeeding period of four years the day of heliacal rising； which marked the true beginning of the yearand which still； of c